Question

Find how many integers between 200 and 500 are divisible by 8

Answer 1

You can solve this problem as an Arithmetic Progression.

The series: 208, 216, 224,...., 488, 496

a(n) = 496
a(1) = 208
d = 8

For an A.P.,
a(n) = a(1) + (n-1)d
=> 496 = 208 + (n-1)8
=> 288/8 = n - 1
=> n = 36 + 1 = 37

Hence, there are 37 such integers.

Answer 2

Find the first number in thist interval that is divisible by 8

In this case:

200 / 8 = 25

Find the last number in thist interval that is divisible by 8

In this case:

496 / 8 = 62

Numbers 200 and 496 assume arithmetic progression, where first member a1 = 200 and last member a62 = 496

Common difference is d = 8

In arithmetic progression:

an = a1 + ( n - 1 ) d

In this case:

a62 = a1 + ( n - 1 ) d

496 = 200 + ( n - 1 ) ∙ 8

496 = 200 + 8 n - 8

496 = 192 + 8 n

Subtract 192 to both sides

496 - 192 = 192 + 8 n - 192

304 = 8 n

Divide both sides by 8

38 = n

n = 38

Answer 3

200 shouldn't be included, should it?

The question says 'between 200 and 500', so.